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    Re: Lunars: A 90 Degree Miracle
    From: George Huxtable
    Date: 2004 Nov 3, 15:46 +0000

    On 1 Nov I posted a message which was somewhat sceptical about Frank's
    Reed's claim, that when a lunar distance equalled 90 degrees, it was
    completely insensitive to error in the altitudes of the bodies involved.
    I wrote-
    >"Take a simple case. The Moon is at an altitude of 45 degrees on one side of
    >the sky. The other body is at 45 degrees on the other side of the sky, so that
    >their azimuths differ by 180 deg. [minor typo fixed]
    >The lunar distance, in that case, is 90 deg. Does Frank claim that in such
    >a geometry, errors in the Moon's altitude correction, resulting from errors
    >in its altitude, would have no effect?"
    And Frank replied-
    >Yes. That's the "miraculous" thing. Errors in the altitude correction are
    >compensated by the change in azimuth. If the objects are "really" both at 45
    >degrees altitude and 90 degrees distance then when I work the calculation
    >I will
    >find that the difference in azimuth is 180 degrees. But if I measure 45 deg for
    >the other body and by some accident measure 40 degrees for the Moon's
    >altitude,  the difference in azimuth will be more like 147 degrees. The
    >change in
    >relative azimuth cancels out the change in the altitude correction.
    I've now tried that, and some other examples, and done a bit of pondering
    about the matter. I am now fully convinced that Frank's analysis was
    correct, and my own understanding was quite wrong.
    So I'm grateful to Frank for making me think rather more deeply about the
    matter, and steering me on the right track.
    contact George Huxtable by email at george---.u-net.com, by phone at
    01865 820222 (from outside UK, +44 1865 820222), or by mail at 1 Sandy
    Lane, Southmoor, Abingdon, Oxon OX13 5HX, UK.

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